Q 1 – The standard form of a linear equation in one variable x is
(a) ax + b = 0
(b) ax² + bx + c = 0
(c) ax³ + bx² + cx + d = 0
(d) ax + bx³ + cx² + dx + e = 0
Ans. (a) ax + b = 0
Q 2 – The difference between two whole numbers is 66. The ratio of the two numbers is 2 : 5. The two numbers are:
a) 60 and 6
b) 100 and 33
c) 110 and 44
d) 99 and 33
Ans. c) 110 and 44
Q 3 – David cuts bread into two equal pieces and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If he has seven pieces of the bread all with him, how heavy is the original cake?
(a) 120 gm
(b) 180 gm
(c) 300 gm
(d) 240 gm
Ans. (d) 240 gm
Q 4 – Of the following, the linear equation in one variable x, is
(d) x² + 2x + 3 = 0
Ans.
Q 5 – The statement ‘on adding 10 in a number, the number becomes 20’ in the form of an equation is
(a) x – 10 = 20
(b) x + 10 = 20
(c) 10x = 20
Ans. (b) x + 10 = 20
Q 6 – Mary was counting down from 34 and Thomas was counting upwards simultaneously, the number starting from 1 and he was calling out only the odd numbers. Which common number will they call out at the same time if they were calling out at the same
speed?
(a) 20
(b) 21
(c) 22
(d) 23
Ans. (d) 23
Q 7 – The degree of the equation x² – 2x + 1 = x² – 3 is
(a) 1
(b) 2
(c) 0
(d) 3
Ans. (a) 1
Q 8 – The statement ‘on adding 10 in a number, the number becomes 20’ in the form of an equation is
(a) x – 10 = 20
(b) x + 10 = 20
(c) 10x = 20
Ans. (b) x + 10 = 20
Q 9 – Find the solution of 2x – 3 = 7
(a) 3
(b) 4
(c) 5
(d) none of these
Ans. (c) 5
Q 10 – The solution of the equation 
is
(a) 10
Q 11 – The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.
Q 12 – Solve 2x – 3 = x + 2
(a) 4
(b) 5
(c) 3
(d) 0
Ans. (b) 5
Q 13 – If 15 is subtracted from a number, it becomes -5. This statement in the form of an equation is
(a) x + 15 = –5
(b) x – 15 = 5
(c) x + 15 = 5
(d) x – 15 = –5
Ans. (d) x – 15 = –5
Q 14 – If 6 is added to 3 times of a number, it becomes 15. This statement in the form of an equation is
(a) 3x + 6 = 15
(b) 3x – 6 = 15
(c) 3x + 15 = 6
Ans. (a) 3x + 6 = 15
Q 15 – Seven times a number is 42. This statement in the form of an equation is
(a) x + 7 = 42
(b) 7x = 42
(d) x – 7 = 42.
Ans. (b) 7x = 42
Q 16 – On subtracting 30 from two times a number, we get 56. This statement in the form of an equation is
(a) 2x – 30 = 56
(b) 2x + 30 = 56
(c) 30 – 2x = 56
Ans. (a) 2x – 30 = 56
Q 17 – Amina thinks of a number and subtracts 5/2 from it. She multiplies the result by 8. The result now obtained is 3 times the same number she thought of. What is the number?
(a) 2
(b) 3
(c) 4
(d) none of these
Ans. (c) 4
Q 18 – A number when subtracted from 40 results into 15. This statement in the form of an equation is
(a) 40 – x = 15
(b) x – 40 = 15
(c) 40 + x = 15
(d) 40x = 15
Ans. (a) 40 – x = 15
Q 19 – The root of the equation 3x = 
– x is
(a) 10
Q 20 – A number when divided by 5 gives 6. This statement in the form of an equation is
(a) x – 5 = 6
(b) x + 5 = 6
= 6
(d) 5x = 6
= 6
Q 21 – The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.
(a) 112
(b) 126
(c) 119
(d) 116
Ans. (a) 112
Q 22 – The root of the equation z + 4 = – 8 is
(a) 3
(b) –32
(c) 12
(d) 4
Ans. (b) –32
Q 23 – The distance between two-mile stones is 230 km and two cars start simultaneously from the milestones in opposite directions and the distance between them after three hours is 20 km. If the speed of one car is less than that of other by 10 km/h, find the speed of each car.
(a) 25 km/h, 40 km/h
(b) 40 km/h, 50 km/h
(c) 20 km/h, 40 km/h
(d) 30 km/h, 40 km/h
Ans. (d) 30 km/h, 40 km/h
Q 24 – The root of the equation 2x + 3 = 2(x – 4) is
(a) 2
(b) 4
(c) 0
(d) does not exist.
Ans. (d) does not exist.
Q 25 – The largest number of the three consecutive numbers is x + 1. Then, the smallest number is
(a) x + 2
(b) x + 1
(c) x
(d) x – 1.
Ans. (d) x – 1.
Q 26 – The difference between two whole numbers is 66. The ratio of the two numbers is 2: 5. What are the two numbers?
(a) 22 and 88
(b) 44 and 66
(c) 44 and 110
(d) 33 and 99
Ans. (c) 44 and 110
Q 27, x is an odd number. The largest odd number preceding x is
(a) x – 1
(b) x – 2
(c) x – 3
(d) x – 4
Ans. (b) x – 2
Q 28 – The difference between the two numbers is 21. The larger number is x. The smaller number is
(a) 21 + x
(b) 21 – x
(c) x – 21
(d) -x – 21.
Ans. (c) x – 21
Q 29 – In a two-digit number, the unit’s digit is x and the ten’s digit is y. Then, the number is
(a) 10y + x
(b) 10x + y
(c) 10y – x
(d) 10x – y
Ans. (a) 10y + x
Q 30 – When 9 is added to two times a number, we get 67. The number is
(a) 25
(b) 27
(c) 29
(d) 31
Ans. (c) 29
Q 31 – What will be the solution of these equations ax + by = a – b, bx – ay = a + b
(a) x = 1, y = 2
(b) x = 2,y = –1
(c) x = –2, y = –2
(d) x = 1, y = –1
Ans. (d) x = 1, y = –1
Q 32 – The value of x in 
= 2x is 3
(c) 3
(d) – 3
Q 33 – An MNC company employed 25 men to do the official work in 32 days. After 16 days, it employed 5 more men and work was finished one day earlier. If it had not employed additional men, it would have been behind by how many days?
(a) 1 day
(b) 2 days
(c) 3 days
(d) 2.5 days
Ans. (b) 2 days
Q 34 – The root of the equation 5x – 8 = 7 is
(a) 1
(b) 2
(c) 3
(d) –3
Ans. (c) 3
Q 35 – Which of the following is not a linear equation in one variable?
(a) 33z + 5
(b) 33 (x + y)
(c) 33x + 5
(d) 33y + 5
Ans. (b) 33 (x + y)
Q 36 – The sum of two numbers is 95. If one exceeds the other by 15, find the numbers.
(a) 40 and 60
(b) 50 and 55
(c) 50 and 60
(d) 40 and 55
Ans. (d) 40 and 55
Q 37 – The root of the equation x – 8 = 2 is
(a) 2
(b) 8
(c) 6
(d) 10
Ans. (d) 10
Q 38 – The sum of a two-digit number and the number formed by interchanging its digit is 110. If ten is subtracted from the first number, the new number is 4 more than 5 times of the sum of the digits in the first number. Find the first number.
(a) 46
(b) 48
(c) 64
(d) 84
Ans. (c) 64
Q 39 – The root of the equation 2y = 5 (3 + y) is
(a) 5
(b) 1/5
(c) –5
(d) –1/5
Ans. (c) –5
Q 40 – Aruna cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty grams
in weight. If she has seven pieces of the cake in all with her, how heavy was the original cake ?
(a) 120 gm
(b) 180 gm
(c) 300 gm
(d) 240 gm
Ans. (d) 240 gm
Q 41 – The root of the equation 14 – x = 8 is
(a) 2
(b) 4
(c) 6
(d) 8
Ans. (c) 6
Q 42 – Three consecutive integers add up to 51. The integers are:
(a) 16,17,18
(b) 15,16,17
(c) 17,18,19
(d) 18,19,20
Ans. (a) 16,17,18
Q 43 – The root of the equation 
= 30 is
(a) 9
(b) 12
(c) 15
(d) 18
Ans. (d) 18
Q 44 – The solution for 3m = 5m – 
is:
Q 45 – The root of the equation 9z – 15 = 9 – 3z is
(a) 1
(b) 2
(c) 3
(d) 4
Ans. (b) 2
Q 46 – The root of the equation 
x = – 27 is
(a) 6
(b) 12
(c) 18
(d) –18
Ans. (d) –18
Q 47 – If two angles are complementary and one angle is 10° greater than the other, then the smaller angle of the two is
(a) 40°
(b) 50°
(c) 90°
(d) 180°.
Ans. (a) 40°
Q 48 – Twice a number is as much greater than 30 as the three times of the number less than 60. The number is
(a) 6
(b) 9
(c) 12
(d) 18
Ans. (d) 18
Q 49 – One number is greater than the other number by 3. The sum of two numbers is 23. The two numbers are
(a) 13, 10
(b) 14, 9
(c) 12, 11
(d) 15, 8s
Ans. (a) 13, 10